2. Assume a Hawk -Dove game with the following payoff matrix, where the first entry isAnimal A's payoff, and the second entry is Animal B's payoff:Animal AHawkDove(rows)/AnimalB (columns)(-5,-5)(0,10)(10,0)(4,4)HawkDoveAn animal that plays Hawk will always fight until it wins or is badly hurt. An animal thatplays Dove makes a bold display but retreats if his opponent starts to fight. If two Doveanimals meet they share.(a) Explain why there cannot be an equilibrium where all animals act as Doves.(b) Explore whether there are any Nash equilibria in pure strategies and explain whichthese are and why.(c) Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawksand Doves? If the proportion of Hawks in the population of animals is greater than themixed strategy equilibrium proportion you calculated, which strategy does better,Hawks of Doves? Explain your answer.

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Assume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A's payoff, and the second entry is Animal B's payoff:

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Question

2. Assume a Hawk -Dove game with the following payoff matrix, where the first entry is
Animal A's payoff, and the second entry is Animal B's payoff:
Animal A
Hawk
Dove
(rows)/Animal
B (columns)
(-5,-5)
(0,10)
(10,0)
(4,4)
Hawk
Dove
An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that
plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove
animals meet they share.
(a) Explain why there cannot be an equilibrium where all animals act as Doves.
(b) Explore whether there are any Nash equilibria in pure strategies and explain which
these are and why.
(c) Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks
and Doves? If the proportion of Hawks in the population of animals is greater than the
mixed strategy equilibrium proportion you calculated, which strategy does better,
Hawks of Doves? Explain your answer.

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